The maximum full and partial likelihood estimators in the proportional hazard model

Summary The maximum full likelihood estimator in the proportional hazard model is explored in relation to the maximum partial likelihood estimator. In the scalar parameter case both the estimators have a common sign, and the absolute value of the former is strictly greater than that of the latter except for trivial cases. We point out also that the maximum full likelihood estimator after a simple modification of the likelihood equation provides a good approximation to the maximum partial likelihood estimator. Similar results are valid for the likelihood ratio tests. The Institute of Statistical Mathematics